Two Ropes, Forty-Five Minutes

The problem
each rope burns in 60 min · unevenlyrope Arope Bmeasure exactly 45 minutes

You have two ropes and a lighter. Each rope, lit at one end, takes exactly 60 minutes to burn through — but they burn unevenly: the first half of a rope might take 58 minutes while the second half takes 2.

Measure exactly 45 minutes. No clock allowed.

Tempting (but wrong)
"burn half the rope = 30 min?"rope A½ the rope ≠ ½ the timeuneven burning blocks geometry tricks

The naïve attempts:

  • "Fold and burn half." Doesn't work — uneven burning means half the length isn't half the time.
  • "Light both ropes at once." Gives you 60 minutes, not 45.
  • "Estimate." No good — the problem asks for exact 45.

The uneven burn rate kills any approach that depends on rope geometry. You need an approach that depends only on the total burn budget of each rope.